1. Field of the Invention
The present invention relates to a method of color reproduction, a method of reproducing a coating color, and a method of selecting a coating color. More particularly, the present invention concerns a method of color reproduction by determining in advance correlations between input values and an outputted color for reproducing a specific color in an apparatus for color printing, color display, or the like, as well as a method of reproducing a coating color and a method of selecting a coating color so as to reproduce a coating color of a coated surface intended by a designer or the like when obtaining a coated surface by coating the surface with a paint or the like or when displaying a coated surface on a color CRT.
2. Description of the Related Art
As is known, the color of an object surface, a color original image, or the like can be specified in a standardized manner by determining the position where chromaticity coordinates, which are expressed by using tristimulus values X, Y, and Z of the color in the CIE (International Commission on Illumination) standard XYZ colorimetric system, are located in a chromaticity diagram. Namely, if the spectral distribution I(.lambda.) of light reflected from or transmitted through the object or the like can be measured, the tristimulus values X, Y, and Z can be determined from the following Formula (1): ##EQU1## where k=100.multidot..intg.{I(.lambda.)y(.lambda.)d.lambda.},
x(.lambda.), y(.lambda.), z(.lambda.): CIE color matching functions, PA1 .lambda.: wavelength
This value Y shows the brightness of the light having I(.lambda.), and the color can be specified by plotting points on a chromaticity diagram of an orthogonal coordinate system, in which values of x and y obtained from the following Formulae (2) are set as chromaticity coordinates, and x is plotted as the abscissa and y as the ordinate in a conventionally known manner (all the colors are included within a slanted bell shape): EQU x=X/(X+Y+Z) EQU y=Y/(X+Y+Z) (2)
Recently, there has been a need for reproduction of colors which can be specified in a standardized manner as described above. For instance, in the field of design, there has been a demand for color-reproducing techniques which make it possible to faithfully reproduce necessary colors for the purpose of evaluation of color design. As examples of apparatus which require color reproduction of color original images, there are display units for displaying color-reproduced images that are color-reproduced on the basis of color data on color original images, as well as color copying apparatus (color hard-copying apparatus) for copying color-reproduced images that are color-reproduced on the basis of color data on color original images.
As a method of color reproduction during color hard copying in the color hard-copy apparatus, a method of color reproduction is known for faithfully reproducing a necessary color by using image processing (Kodera: "Image Processing for Color Reproduction" in Supplementary Volume "Imaging Part 1" of the Shashin Kogyo (Photo Industry) published by Shashin Kogyo and compiled by the Electrophotography Society).
However, since the color can be specified by the mixing of pigments of YMC colors, RGB signals for the display, or the like, the RGB colorimetric system based on the three primary colors (reference stimuli) is in most cases used as the colorimetric system for specifying actual colors. Hence, conversion of color data in the RGB colorimetric system to and from color data in the XYZ colorimetric system is required.
By taking the aforementioned color copying apparatus as an example, color specification in this color copying apparatus is generally effected by mixing predetermined color materials (R material, G material, and B material) to form a reproduced image (a copy of the original) and output the same. Because respective colors of this reproduced image can be specified by data in the XYZ colorimetric system, i.e., color data using the tristimulus values X, Y, and Z, on the basis of reproducing conditions such as a mixing ratio of the color materials and values of measurement by a spectrophotometer or the like, each of these colors may be considered as a function f for computing the tristimulus values X, Y, and Z using data (r, g, and b) of the color materials as parameters, as shown in the following Formula (3): EQU f: (r, g, b).fwdarw.(X, Y, X) (3)
Since the density based on these color materials can generally be changed in 256 gradations for r, g, and b, respectively, it is possible to reproduce a color original image in 256.sup.3 (=16,777,216) combinations.
Here, since the color data when the color original image is read can be converted to color data in the XYZ colorimetric system, as described above, it is possible to compute the tristimulus values X, Y, and Z of the colors to be reproduced as a reproduced image. Accordingly, if the data (r, g, and b) of the color material, in which the tristimulus values X, Y, and Z, i.e., output values of the function f, are equal to the tristimulus values X, Y, and Z of the color data on the color original image, are determined, color reproduction is possible with high accuracy. For this reason, it is possible to form a reproduced image with a high level of color reproducibility by determining an inverse function f.sup.-1 of Formula (3) in advance and then by using the data (r, g, and b) on the color material determined by this inverse function f.sup.-1.
However, in the aforementioned color copying apparatus, since color formation is generally based on the subtractive mixture of color stimuli, Formula (3) above becomes nonlinear. For this reason, it is difficult to determine the inverse function f.sup.-1. To overcome this problem, it is conceivable to determine and store in advance all of the tristimulus values X, Y, and Z and the data on the color materials with respect to the 256.sup.3 combinations mentioned above and to extract data on the color materials which are in a relationship of the inverse function f.sup.-1 during reproduction processing. However, the amount of computation for processing in advance is enormously large, and a storage area for storing the relationships determined also becomes enormously large, so that this scheme is not practically feasible.
In addition, an object surface, such as the body of a vehicle, is formed by a coated surface having a coating color obtained by applying a paint or the like. To obtain a coated surface of a desired coating color intended by a user, a designer, and the like, a paint or the like obtained by mixing a plurality of pigments and the like by using a color sample as a reference is applied to the object.
A method is conventionally known in which, with respect to an object surface having uniform optical properties, the color of the object is reproduced and displayed three-dimensionally and realistically with accuracy with the semblance of the actual object by computing coloring on the basis of a ray tracing method using the reflectance of the object surface, such as the spectral reflectance factor (A. Takagi et al. "Computer Graphics," Vol. 24, No. 4, 1990, and the like). In this method, color specification values (tristimulus values) of the CIE standard XYZ colorimetric system are first determined on the basis of a spectral reflectance factor and the like of the object surface. These tristimulus values are then converted to color specification values peculiar to the colorimetric system through a linear combination transformation, are subjected to .gamma. correction, and are converted to RGB gradients, thereby reproducing the object color and displaying an image. According to this method, if the reflectance of the object can be specified, it is possible to reproduce and display the object color. At the same time, the reflectance of the object corresponding to the displayed color can be specified by processing in the reverse order, and virtual color components for obtaining the displayed color can be determined. It is possible to obtain a desired coating color, if the object is coated with a paint or the like obtained by mixing a plurality of pigments and the like in quantities corresponding to the quantities of these color components.
However, the setting of a ratio of mixing or compounding pigments for obtaining the desired coating color requires the trained skill of a technician, and is very low in productivity. In addition, it does not necessarily follow that the coating color on the finished coated surface can always be reproduced to the coating color intended by the user, the designer, and the like owing to differences and variations in the type of component materials such as pigments.
To overcome this problem, computer color matching (hereafter referred to as CCM) has been widely used in which compounding involving the setting of a mixing ratio of pigments, which requires trained skill, is determined by computation by a computer in compounding basic color materials (coloring agents such as pigments) in accordance with the Kubelka-Munk's theory. In this CCM, the mixing ratio and the like of a plurality of pigments whose reflectances are known are determined by computation by a computer, such that the reflectance will be equal to the reflectance of a color sample measured by a spectrophotometer or the like. In another case, the mixing ratio and the like of a plurality of pigments whose tristimulus values are known are determined by computation by a computer, such that the tristimulus values will be equal to the tristimulus values of the color sample. Thus, a method is known for determining the mixing ratio and the like of coloring agents by using CCM so as to reproduce an intended coating color (Japanese Patent Application Laid-Open No. 149760/1987).
With the conventional methods of reproducing a coating color using CCM, however, since compounding is determined in accordance with the Kubelka-Munk's theory, it is impossible to effect compounding by mixing substances whose surface reflectances do not conform to the Kubelka-Munk's theory. In addition, it is impossible to specify a coating color which includes bright materials such a metallic paint and mica as its component materials.
In addition, although the above-described CCM is effective in obtaining a coating color which coincides with a color sample or the like, reflectance values and tristimulus values for specifying the coating color are not subjective. Therefore, it is difficult for the above-described CCM to reflect trends of sensuous coating colors, such as reddish and glossy colors, which are used by designers and the like as specification for obtaining desired coating colors from already existing coating colors.